Introduction: Quantum Fluctuations In Light Of Exponentiation: Our base-2 exponentiation chart  from the Planck base units to the Observable Universe and Age of the Universe has 202 notations. It is logical and simple. Yet, to qualify as a potential alternative to big bang cosmology, it will have to do everything the big bang seems to do well, and go beyond it in addressing other open questions. One such question is regarding quantum fluctuations. Considered to be a random change of energy in a point in space described by Heisenberg uncertainty principle, within this model that “point in space” is much larger than currently accepted. In our mathematical and geometrical model based on the Planck units, fluctuations are projected to be in the range of the Notations 55-to-67. The first “points” are transformation points between the finite and infinite smaller than the Planck base units. The so-called points within the core physics curriculum have values defined by the Planck base unit multiples from Notation-1 through to at least Notation-64, perhaps as high as Notation-67.
Background. In December 2011, this project began by following embedded geometries, smaller and smaller, by dividing the edges of the tetrahedron by 2 and then also the octahedron, connecting the new vertices. In 45 steps doing a Zeno-like progression further and further within, we were in the domain of particle physics. In another 67 steps within we were in the domain of the Planck scale. In our naïveté we then multiplied our little tetrahedron by 2, and in 90 steps were out to the age and size of the universe.
Today, it is a mathematical and geometrical model based on the Planck’s natural units.
Why didn’t Max Planck and Albert Einstein do the simple math? Why it took the extreme naïveté of high school people is anybody’s guess. It seems logical. It looks logical. Since 2011, we have asked hundreds of our best scholars for advice. Very little has been given. We know this much. Geometry and mathematics are real realities and Aristotle made a mistake when he thought one could tile the universe with just tetrahedrons.
Aristotle’s missed gap may be the most seminal gap. Since Aristotle, it appears that the world of scholarship also missed the corollary five-octahedral gap. It is the same gap but made with octahedrons. The composite with the two is a striking image.
There are other gaps. Icosahedral gaps are dramatic. Given the lack of understanding in this realm of physics, we postulate and hypothesize that these gaps, once they’ve became systemic, start the earliest fluctuations in the universe.
The first-possible physical measurements in our universe happen in labs like CERN (Geneva, Switzerland). Estimates of the ionic radius involved in their heavy ion collisions range from 30-to-300 picometers or approximately 3.9077×10-11 meters (Notation-81) to 3.12618×10-10 meters (Notation-84). It appears that the collider experiments result in measurements within the scale of the 67th notation (2.38509×10-15 meters), the 66th notation (1.19254×10-15 meters) yet some say down as small as 1.16459×10-18 meters at the 56th notation. These and the other numbers in the 202 columns are real numbers, all multiples of the Planck base units.
Today these numbers are all just simple mathematics and imputed geometries and this system of numbers is not yet recognized by the scholarly community to be meaningful or significant.
Potential Significance: By themselves these numbers create a rich panoply of possibility. We believe it would be unimaginative not to try to do something with them, so we enter the domain of the mysterious quantum fluctuations. Unlike current theorists, their “out of nothing” is for us as many as 67 notations where distinctions between notation 2-to-66 are expected to be as great as those within the next 67 notations (67-134), and then again within the next 67 (134-201) that follow.
Pi And Never-ending, Non-repeating Numbers. The animated image (on the right) challenges us in unusual ways. Looking for other possible parts of the puzzle, we accept the logic and necessity of a singularity, but conclude that it is a dynamic transformational nexus between the finite and infinite whereby there is a complete unification of all the basic forces of nature, the Planck base units (aka Planck scale), the dimensionless constants, and a very special class of circles and spheres.
That is our working hypothesis. We further postulate that this working premise creates an environment to build a panoply of bridges from the Planck scale to all current physical theories whereby each notation is a domain for unique predictive values. The challenge will be to recognize the mechanisms that would confirm or deny these hypotheses and postulations.
Fact Gathering: The Tools of this Art. The first thing we did was look for the possible parts of the puzzle. Of course, there are the Planck base units. There are the 202 notations. There is the speed of light — Planck Length divided by Planck Time — within each and every notation. These are starting points.
The universe appears to be logically divided into three scales. The small scale from notations 2-67, the human-scale from 67-to-134, and the large scale from 134-to-201.
The next big observation is that the progression of epochs defined by big bang cosmology is well-defined by a natural inflation within base-2 exponentiation. Simple logic seems to suggest that each currently-defined big bang epoch can readily become a process within the base-2 model. And, significantly, there is no need for an actual big bang; natural inflation is quite enough.
Within our Top Ten Reasons to Put Big Bang Cosmology In Time Out, we now turn to a few of the many enigmatic questions within cosmology. Perhaps within the base-2 model we can find answers or something new.
More Postulations. These first 67 notations could be the deep systems structure of the universe that give rise to richly-textured quantum fluctuations, cosmic microwave background radiation (CMBR), homogeneity and isotropy, dark energy and dark matter, magnetism, and gravity (defined by General Relativity). Big bang cosmology has no answers. Given that the base-2 model is simple, it may hold rather simple answers. This article is our first to enter this configuration space starting at notations 0,1 with a point (vertex), then a line, a circle, a sphere, a tetrahedron, and then tetrahedrons and octahedrons. That animated image (top left) demonstrates a process that apparently has not been studied much beyond the problem of stacking cannonballs. (Thomas Hales followed up Thomas Harriot’s work)
The Art: Using dimensional analysis within the first 21 notations, there are over a quintillion base-8 vertices with which to experiment and build initial systems! Sophus Lie could make millions of his E8 structures. Within just the first ten notations, there are 134,217,728 scaling vertices. Possible analogues include the protein machines or nanomachines within the body. Other analogues could include genetic code machines.
The first ten notations. We’ll call them axiomatic machines (systems) that extend the continuities inherently defined by Planck base units (length, time, mass, and charge). `These axiomatic machines are also defined by the speed of light (or special relativity), the gravitational constant (or general relativity), the reduced Planck constant (or ħ or quantum mechanics), the Coulomb constant (or ε0 or electric charge or electromagnetism), and the Boltzmann constant (or kB or temperature). All “things” within these notations are uniquely defined by pi. These are not physical things; these are ontological things, or perhaps axiomatic things. We will be working on the nomenclature as we go along this path.
So, let’s build some simple mechanisms, then work with the art (and magic) to bring all that richly-textured phenomena of the universe to life! Let’s see what we can do with the most artistic and unpredictable of that group, quantum fluctuations.
Transformation Nexus. Once the singularity is multiplied by 2 (the form) or by 8 (the function), it is no longer the Planck singularity or Planck Epoch; it becomes the first possible transformation nexus between the finite and infinite.
Could it be that from this beginning, everything, everywhere, shares these eight vertices. “Ridiculous? Poppycock?“
We ask that you hold those judgments in abeyance. To get into this model will require stretching, suspending judgment and imagining in rather new ways. With eight vertices the universe might organize those vertices as five tetrahedrons with a small space between the fifth and first tetrahedron. There is one extra vertex. It is elegant. It is imperfect. It creates degrees of freedom (7.356103 degree gap or 0.12838822 radians).
Couldn’t this be the birthplace, the earliest beginning of the quantum fluctuation?
Could this possibly be a key process that is extended throughout all 202 notations? Of course, those who know molecular geometry readily recognize the figure.
In the next doubling there are 64 vertices. Seven-plus-1 is established. The next 13 vertices extending from “The Seven” create a mathematically whole figure, an absolute figure of six tetrahedrons whereby there is potential action because the base is a perfect structure, a hexagonal plate.
Each cannonball is a vertex. Or, is it an infinitesimal circle or sphere? …both? Given that we are working with the five basic Planck units with real numbers that define each unit, the vertices are 134,217,728 scaling vertices. a real manifestation within space-and-time.
The animated image (gif for “Graphics Interchange Format”) of the cannonball stack tells a powerful story.
The all-important quantum fluctuation seems like an art form on one hand and a fundamental energy source on the other. Open this conceptual roadblock and we find a truly golden rainbow. Although each roadblock is a face of this small-scale universe, perhaps quantum fluctuations would best be known as the art of the universe!
The most important fact about the new model is that each of the Epochs defined within Big Bang Cosmology are all logically replicated here. All of our data is simple math and it is a fully predictive model of the universe without the bang! Numbers
The world’s leading cosmological theory is challenged. Though our little model is little-known today, that is about to change. Big bang cosmology is going to be placed on ice and assigned to timeout.
The Art, Mechanics & Systems
Let’s start at the very beginning: Notations 1-10
PLEASE OPEN THE CHART IN A NEW WINDOW.
Each of the Planck base units, considered to be part of the so-called singularity, has a real number associated with it. Though the formulas for deriving the numbers of each Planck base are readily understood by many, watching how the numbers progress along their scale is new.
In the first ten notations, we first assumed the numbers represented vertices that will double and slowly become structure.
Endnotes & Footnotes
There may not be many because all these points already have pages within this website.
. In process, November 7, 2022
 In process, November 7, 2022
 In process, November 7, 2022
References & Resources
As these references are studied, key references and resources will be added.within this website.
There will also be many instant messages to thought leaders about the key points.
2:25 PM · Nov 7, 2022 Geraint F. Lewis, @Cosmic_Horizons @Sydney_Uni Go inside the tetrahedron (divide the edges by 2, connect new vertices) and in 67 steps you’ll be at the Planck base units. Now multiply by 2, 202 times and you have the universe: https://81018.com A little math and geometry go a long way!
• This page may someday become a homepage. Today it is very much “under construction.”
• The last update was November 7, 2022.
• This page was initiated on January 17, 2017.
• The URL for this file is https://81018.com/flucutations/
• The working title is: Quantum Fluctuations
• The top-left tagline: Alternatives to Big Bang Cosmology
• Is the Big Bang Boom Over
• Is there an implosion already underway?
• Quiet Expansion possible?
• Alternatives to Big Bang Cosmology
• Correspondence to Hawking, Guth and Andrei Linde
• Correspondence to the Director General, CERN, Geneva